Method and system for analyzing diffraction data from crystalline systems

Abstract

A method and system for indexing powder diffraction data are disclosed comprising choosing a maximum impurity peak tolerance level for a crystallography data search, choosing a range of number of calculated peaks for possible indexing solutions having a minimum number of peaks and a maximum number of peaks, selecting a crystal system to search, selecting powder extinction classes to search for indexing solutions, performing an exhaustive unit cell search of each of the selected powder extinction classes using a successive dichotomy approach to determine a set of indexing results, and ranking the obtained solutions according to likelihood.

1. A method of indexing powder diffraction data, comprising:
 choosing a maximum impurity peak tolerance level to limit the search for indexing solutions to those where the number of unindexed peaks lies within the tolerance level;  
 choosing a range for the number of calculated peaks to limit the search for indexing solutions to those where the number of calculated peaks falls within the chosen range;  
 selecting a crystal system to search;  
 selecting a powder extinction class to search for indexing solutions; and  
 performing a unit cell search of the selected powder extinction class using a successive dichotomy approach to determine a set of indexing results.  
 
   
   
     2. A method for exploiting space group symmetry in the indexing of powder diffraction data, by selecting a crystal system to search, then grouping possible indexing solutions compatible with this crystal system into powder extinction classes having the same pattern of systematic absences, and performing separate indexing solution searches within at least two of said powder extinction classes. 
   
   
     3. The method of  claim 2 , wherein said separate indexing solution searches are performed with a successive dichotomy method. 
   
   
     4. The method of  claim 2 , wherein said separate indexing solution searches are limited to searching for solutions having a preselected maximum number of calculated reflections. 
   
   
     5. A system for indexing a set of powder diffraction data, comprising: a general purpose processor, wherein the processor is configured to divide the data into a plurality of powder extinction classes having the same pattern of systematic absences, and wherein the processor is further adapted to search each powder extinction class over a calculated peak number range. 
   
   
     6. A system for indexing a set of powder diffraction data, comprising:
 a memory storing diffraction data; and  
 at least one processor configured to read data from and write data to the memory and further configured to analyze said data to produce indexing solutions starting at solutions with a small number of calculated peaks and progressing toward solutions with a larger number of calculated peaks.  
 
   
   
     7. The system of  claim 6 , wherein said processor is configured to perform a series of separate successive dichotomy searches using a corresponding series of calculated peak number ranges. 
   
   
     8. A method of analyzing diffraction data comprising:
 generating a plurality of indexing solutions from said diffraction data;  
 ranking said indexing solutions by calculating a figure of merit for at least some of said indexing solutions, wherein said figure of merit is constructed such that it tends to rank solutions with smaller numbers of calculated reflections higher.  
 
   
   
     9. The method of  claim 8 , wherein said figure of merit comprises the expression N obs /N calc , wherein N obs  is the number of measured reflections in said diffraction data, and N calc  is the number of calculated reflections for the ranked indexing solution. 
   
   
     10. The method of  claim 8 , wherein said figure of merit tends to rank highly solutions with a smaller number of fitted parameters. 
   
   
     11. The method of  claim 8 , wherein said figure of merit F a  is of the form: 
         F   a     ∝         θ   _              Δ   ⁢           ⁢   θ          _       ⁢       N   obs       N   calc       ⁢     1     N   par             
 wherein N obs , is the number of measured reflections in said diffraction data, and N calc  is the number of calculated reflections for the ranked indexing solution, N par  is the number of fitted parameters producing the solution, {overscore (θ)} is average observed peak position, and {overscore (|Δθ|)} is the average absolute difference between the calculated and the observed peak positions.  
 
   
   
     12. The method of  claim 11 , additionally comprising normalizing said figure of merit relative to an approximate expected average figure of merit produced from a randomly selected incorrect indexing solution. 
   
   
     13. A system for indexing powder diffraction data, comprising:
 means for choosing a maximum impurity peak tolerance level for a crystallography data search;  
 means for choosing a range of number of calculated peaks for possible indexing solutions having a minimum number of peaks and a maximum number of peaks;  
 means for selecting a crystal system to search;  
 means for selecting a powder extinction class to search for indexing solutions; and  
 means for performing an exhaustive unit cell search of the selected powder extinction class using a successive dichotomy approach to determine a set of indexing results.  
 
   
   
     14. The apparatus of  claim 12 , additionally comprising means for ranking and comparing indexing solutions for powder diffraction data corresponding to different extinction classes using a figure of merit designed to rank highly the most likely solutions.